Texture Coming off Drywall Ceiling

W/o seeing a chip, it's hard to say why it was incorrectly done
Most likely no primer, but could have been failure to clean off sanding dust, incorrect or bad primer (Kilz2), etc...
Regardless, the solution is to take down any/all poorly adhering texture
Scraping and sanding are usually the best way

What you have left will determine the best action
Most likely it will be a coat of penetrating problem solving primer, then texture or skim coat depending on what's left and what you want

Texture Coming off Drywall Ceiling

Wow, that is all kinds of Epic Fail there...

Just looking at your pictures, it looks like the texture is cleanly separating from the drywall underneath. It appears that the drywall facing itself is intact. Unless they used Gardz on this ceiling for no particular reason, that is pretty darn unprimed.

I can't imagine that even the awful Kilz2 is so staggeringly bad that it would cleanly separate from the facing like that.

Scrape, prime with a quality primer, and you should be good to go to re-coat.